Researchers from the Laboratory for Fluid Dynamics and Thermodynamics, Faculty of Mechanical Engineering, and the Laboratory for Simulation of Materials and Processes, Institute of Metals and Technology have developed a new meshless solution of the governing equations of elasto-plasticity. Meshless methods represent a new generation of discretisation techniques for solving partial differential equations. The new method, based on strong formulation, combines the finite difference method with the meshless local radial basis function collocation method (LRBFCM), structured with the polyharmonic splines. This combination solves the elasto-plastic problems previously unsolvable with the LRBFCM approach only. The results of their research have been published in the journal “Computer Methods in Applied Mechanics and Engineering” (IF=7.2), a primary journal in the field of Computational Mechanics.
The study provides a detailed analysis of the influence of free parameters on the accuracy, stability, and convergence of this novel approach.
The new approach avoids the meshing and integration process. Its coding complexity is similar in two and three dimensions.
The industrial application of the described novel method is foreseen in different thermomechanical simulations of aluminium alloys and steel production processes.
The article is available at: https://doi.org/10.1016/j.cma.2023.116501